Hybrid assessment method for LES models

LES is the study of turbulent flows obtained by resolving only the largest scales of Navier-Stokes equations. The restriction to the largest scales is equivalent to the application of a low pass filter, denoted by the overbar symbol

$\overline{\dots}$

, on the equations. We solve the equations for the filtered incompressible velocity field

$\overline{u}_{i}$

:

where

ν

is the kinematic viscosity of the fluid. The difference between the original and the LES Navier-Stokes equations comes from the so-called subgrid-scale stress tensor:

$\tau_{ij} =\overline{u_{i}u_{j}}-\overline{\overline{u}_{i}\overline{u}_{j}}$

acting only via the gradient of its traceless tensor

$h_{i}=\partial_{j}\tau^{\star}_{ij}$

. Its exact value cannot be computed, it is needed to approximate the exact tensor

$\tau^{\star}_{ij}$

by a subgrid-scale model tensor

$\tau^{\star}_{ij}\approx \tau^{\textrm{\tiny M}}_{ij}(\overline{u}_{l}) $

. The present study proposes a new framework to assess the LES models. So far, the assessment of subgrid-scale model relies either on a priori or a posteriori methods.